This document summarizes the computation of transonic turbulent flow past an ONERA M6 wing using different turbulence models in HiFUN solver. It presents results on lift and drag coefficients from Spalart-Allamaras, SST k-omega, and TNT k-omega models. Cp plots and Mach/pressure contours at various angles of attack are shown and compare well to experimental data, validating the solver. The document concludes HiFUN's parallel processing, variable CFL ramping, and robust turbulence models enable fast and accurate computation of this transonic turbulent wing flow.

1. COMPUTATION OF
TRANSONIC TURBULENT FLOW PAST
ONERA M6 WING
Presented By:
Atin Kumar
M.Tech CFD
University of Petroleum and Energy Studies
Dehradun, India
Guided By:
Dr. Munikrishna N.
Chief Technology Officer (CTO)
S & I Engineering Solution Pvt. Ltd.
Bangalore, India

2. 1) Objective
2) Introduction
3) Simulation parameters
4) Results & Discussion
4.1) Cp Plots
4.2) Mach Number & Pressure Contour
4.3) Number of Iterations & Ramping Options
4.4) Convergence Study
5) Conclusion

3. Objective
– Computation of transonic turbulent flow past ONERA M6 wing
using different turbulent models available with HiFUN solver.
■ Spalart Allamaras: for two different conditions available in HiFUN
namely:
– Low Reynolds number variant
– Default model (FV3 variant)
■ SST K-Omega
■ TNT K-Omega
– To validate the obtained results against experimental results
data provided by Volker Schmitt and François Charpin in 1979 (ONERA scientists).

4. Introduction
– Arrow shaped configuration designed by Bernard Monnerie and
his aerodynamicist team at French Aerospace research lab
“Office National d'Etudes et de Recherches Aérospatiales
(ONERA)” in 1972.
– Aim was to design a wing configuration that mimic the actual
flight conditions.
– well accepted due to geometric simplicity along with transonic
flow complexities i.e. shock-shock interaction, local subsonic
flow, & turbulence boundary layer separation.

5. SimulationParameters Parameters Value
Angle of Attack α 3.06
Mach number M∞ 0.84
Reynolds number Re∞ 11.72 Mil
Temperature T∞ 273.15 K
Thermal Conductivity K 0.024085 W/m-K
Dynamic Viscosity μ ∞ 1.7238e-5 Kg/m-S
Velocity V∞ 278.281832 m/s
Density ρ∞ 0.725988Kg/m3
Pressure P∞ 56913.16474 Pa
Turbulent Kinetic Energy K 9.8776 e-04 m2/s2
Turbulence K. E. Dissipation
Rate
Ѡ 4622.25 s-1
Table 2: Flow Parameters
Parameters Value
MAC 1 m
Reference area of wing 1 m2
Moment reference point 1 m2
Type of Mesh Prism & Tetrahedrons
Total Elements 2537964
Total Nodes 1074476
Scale Factor 0.001
Table 1: Geometric and Mesh parameters
Symmetric Plane(Blue) -> Symmetry
Farfield(Black) -> Riemann Farfield
Wing(Gray) -> Adiabatic
wall
2D Wing Geometry
(SolidWorks)
Mesh

6. Results &
Discussion

7. CoefficientofLift&Drag
Models for simulation Coefficient of Drag Coefficient of Lift
Spalart- Allamaras
(Low Reynolds number variant) 0.024185 0.314490
Spalart- Allamaras
(Default variant)
0.024084 0.315213
SST K-Omega 0.024228 0.306978
TNT K-Omega 0.023366 0.315308
Table 3: Coefficient of Lift & Drag

8. Cp Plots
-1
-0.5
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.2_SA_DEFAULT_VARIENT
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.44_SA_DEFAULT_VARIEN
T
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.65_SA_DEFAULT_VARIEN
T
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.80_SA_DEFAULT_VARIEN
T
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.90_SA_DEFAULT_VARIEN
T
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.95_SA_DEFAULT_VARIEN
T
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.99_SA_DEFAULT_VARIEN
T
Spalart-Allamaras:FV3Variant

9. Spalart-Allamaras:FV3Variant
Mach Number & Pressure Contour Plot

10. -1
-0.5
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.20_SA_LOW_RE_V
ARIENT
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.44_SA_LOW_RE_V
ARIENT
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.65_SA_LOW_RE_V
ARIENT
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.80_SA_LOW_RE_VARIEN
T
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.90_SA_LOW_RE_VARIEN
T
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.95_SA_LOW_RE_VARIEN
T
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.99_SA_LOW_RE_VARIEN
T
Spalart-AllamarasLowReVariant
Cp Plots

11. Spalart-AllamarasLowReVariant
Mach Number & Pressure Contour Plot

12. -1
-0.5
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.20_SST_K_OMEGA
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.44_SST_K_OMEGA
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.65_SST_K_OMEGA
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.80_SST_K_OMEGA
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.90_SST_K_OMEGA
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.95_SST_K_OMEGA
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.99_SST_K_OMEGA
SSTK-Omega
Cp Plots

13. Mach Number & Pressure Contour Plot
SSTK-Omega

14. -1
-0.5
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.20_TNT_K-OMEGA
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.44_TNT_K-OMEGA
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.65_TNT_K-OMEGA
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.80_TNT_K-OMEGA
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.90_TNT_K-OMEGA
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.95_TNT_K-OMEGA
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
CP
X/C
Ŋ=0.99_TNT_K-OMEGA
TNTK-Omega
Cp Plots

15. TNTK-Omega
Mach Number & Pressure Contour Plot

16. Convergence Study-Convergence History, Integrated force & Moment coefficient
SA FV3 Variant SA Low Re Variant SST K-Omega TNT K-Omega
Maximum Iteration – 551 Maximum Iteration – 551 Maximum Iteration – 629 Maximum Iteration – 544
Maximum CFL – 3.85 Million Maximum CFL – 3.85 Million Maximum CFL – 5 Million Maximum CFL – 3.26 Million
MomentCoefficientForceCoefficientConvergenceGraph

17. Number of Iteration and Ramping Options
Start
Iteration
End Iteration CFL Multiplication Factor
1 50 1.0
51 100 50.0
101 150 100.0
151 200 250.0
201 250 500.0
251 300 1000.0
301 350 1500.0
351 400 3000.0
401 450 4000.0
451 500 5000.0
501 550 6000.0
551 600 7000.0
601 651 8000.0
661 700 9000.0
EffectofCFLNumberonSolution
 For SA Low Re Variant simulation, Simulation was performed
for Two different CFL multiplication factor
 Low CFL multiplication & Ramping
 High CFL Multiplication (1 Million)

18. Conclusion
■ Parallel processing capability along with the continuously varying CFL number and
the Ramping factor helped to achieve FASTer convergence.
■ Study performed using different models available in HiFUN and they are almost
overlapping each other reflects the ROBUSTNESS of the commercial CFD solver
HiFUN.
■ Validation against the experimental results are in close agreement with the
calculated HiFUN numbers this results in ACCURACY of HiFUN solver.

19. THANK YOU